In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 32 yards and b = 24 yards, what is c? If necessary, round to the nearest tenth.
c = _____ yards
Question & Answer
What is the length of the hypotenuse in a right triangle with legs measuring 32 yards and 24 yards?
2 Answers
Verified archiveTo find the length of the hypotenuse ( c ) in a right triangle, we can use the Pythagorean theorem, which states:
[ c^2 = a^2 + b^2 ]
Given ( a = 32 ) yards and ( b = 24 ) yards, we can plug in the values:
1. Calculate ( a^2 ):
[
a^2 = 32^2 = 1024
]
2. Calculate ( b^2 ):
[
b^2 = 24^2 = 576
]
3. Now, add these two results:
[
c^2 = 1024 + 576 = 1600
]
4. Finally, take the square root to find ( c ):
[
c = sqrt{1600} = 40 text{ yards}
]
So, the length of the hypotenuse ( c ) is 40 yards.
To find the length of the hypotenuse ( c ) in a right triangle when the lengths of the legs ( a ) and ( b ) are given, you can use the Pythagorean theorem, which states:
[
c^2 = a^2 + b^2
]
Given:
– ( a = 32 ) yards
– ( b = 24 ) yards
Now, substitute the values:
[
c^2 = 32^2 + 24^2
]
Calculating ( 32^2 ) and ( 24^2 ):
[
32^2 = 1024
]
[
24^2 = 576
]
Now, add these two results:
[
c^2 = 1024 + 576 = 1600
]
To find ( c ), take the square root of ( 1600 ):
[
c = sqrt{1600} = 40
]
So the length of the hypotenuse ( c ) is ( 40 ) yards.
Final answer:
c = 40 yards.